If you have regular triangles and hexagons, is there any way to put them together to fill the plane?
You begin by finding the angles at the corners of a regular triangle with interior angle formula. That gives you
which means that the interior angles of a regular triangle are °.
Next, you find the interior angles of a regular hexagon with the same formula. You get
which means that the interior angles of a regular hexagon are °.
If you put two triangles and two hexagons next to each other so that they meet at one point, you can see that the sum of the angles at that point is
That means you can use two regular triangles and two regular hexagons to fill the planar space.